Modern Machine-Shop Practice, Volumes I and II - Joshua Rose

TABLE OF TABULAR VALUES WHICH, MULTIPLIED BY THE ARC PITCH OF THE TEETH, GIVES THE SETTING NUMBER ON THE GRADUATED EDGE OF THE INSTRUMENT.

Ratios.[7]				Number of Teeth in Wheel Sought; or, Wheel for Which Teeth are Sought.
				8	12	16	20	30	40	50	60	70	80	90	100	120	150	200	300	500
				For Faces: Flanks Radial or Curved.
				Draw Setting Tangent at Middle of Tooth.—Epicycloidal Spur or Bevel Gearing.
	¹⁄₁₂	=	.083	.32	.39	.46	.51
	¹⁄₄	=	.250	.31	.37	.44	.49	.61	.70	.78	.85	.92	.99	1.05	1.11	1.22	1.36	1.55	1.94	2.54
	¹⁄₂	=	.500	.28	.34	.41	.46	.57	.66	.73	.80	.87	.93	1.00	1.06	1.15	1.29	1.50	1.86	2.41
	²⁄₃	=	.667	.27	.32	.38	.43	.54	.62	.70	.77	.83	.89	.95	1.01	1.11	1.24	1.45	1.79	2.32
	1			.23	.28	.34	.39	.49	.58	.65	.72	.78	.83	.89	.94	1.03	1.15	1.36	1.65	2.10
	³⁄₂	=	1.50	.19	.25	.29	.34	.44	.51	.58	.64	.69	.74	.79	.84	.93	1.05	1.25	1.53	1.94
	2			.17	.22	.26	.30	.38	.46	.53	.59	.63	.68	.72	.76	.84	.95	1.13	1.40	1.81
	3				.16	.19	.23	.31	.38	.44	.49	.53	.57	.60	.63	.71	.82	.97	1.23	1.60
	4				.14	.17	.20	.26	.33	.38	.42	.46	.49	.53	.56	.63	.73	.87	1.08	1.42
	6							.22	.26	.30	.34	.37	.41	.44	.47	.53	.61	.71	.90	1.20
	12								.20	.23	.25	.28	.30	.32	.34	.37	.42	.49	.60	.82
	24													.19	.21	.23	.26	.31	.40	.57
				For Flanks, when Curved.
				Draw Setting Tangent at Side of Tooth.—EpicycloidalSpur and Bevel Gearing. Faces of Internal, and Flanks of Pinion Teeth.
De-	—	1.5	slight.	.77	.98	1.18	1.36	1.75	2.05	2.31	2.56	2.75	2.92	3.08	3.24	3.52	3.87	4.51	5.50	7.20
gree		2	good.	.44	.54	.63	.72	.92	1.09	1.24	1.38	1.49	1.59	1.79	1.79	1.98	2.23	2.67	3.22	4.50
of		3	more.	.20	.28	.35	.40	.54	.65	.76	.86	.95	1.02	1.10	1.18	1.31	1.46	1.67	2.08	2.76
flank		4	much.		.20	.23	.25	.34	.42	.51	.59	.66	.71	.77	.82	.92	1.06	1.25	1.64	2.15
cur-		6				.16	.17	.26	.32	.38	.43	.48	.52	.56	.60	.66	.76	.93	1.20	1.54
va-		12						.19	.24	.28	.31	.34	.36	.38	.40	.45	.52	.63	.80	.98
ture		24													.22	.25	.28	.33	.47	.60
For Faces of Racks; and of Pinions for Racks andInternal Gears; for Flanks of Internal and Sides of Involute Teeth.
Draw Setting Tangent at Middle of Tooth,regarding Space as Tooth in Internal Teeth. For Rack use Number of Teeth in Pinion.
Pinion.				.31	.39	.48	.57	.73	.88	1.00	1.10	1.20	1.30	1.40	1.48	1.65	1.85	2.15	2.65	3.50
Rack.				.32	.38	.44	.50	.62	.72	.80	.87	.93	.99	1.03	1.08	1.16	1.27	1.49	1.86	2.44

[7] These ratios are obtained by dividing the radius of the wheel sought by the diameter of the generating circle.

From these tables may be found a tabular value which, multiplied by the pitch of the wheel to be marked (as stated at the head of the table), will give the setting number on the graduated edge of the instrument, the procedure being as follows:—

For the teeth of a pair of wheels intended to gear together only (and not with other wheels having a different number of teeth).

For the face of such teeth where the flanks are to be radial lines.

Rule.—Divide the pitch circle radius of the wheel to have its teeth marked by the pitch circle radius of the wheel with which it is to gear: or, what is the same thing, divide the number of teeth in the wheel to have its teeth marked by the number of teeth in the wheel with which it is to gear, and the quotient is the “ratio.” In the ratio column find this number, and look along that line, and in the column at the head of which is the number of teeth contained in the wheel to be marked, is a number termed the tabular value, which, multiplied by the arc pitch of the teeth, will give the number on the graduated edge by which to set the instrument to the tangent line.

Example.—What is the setting number for the face curves of a wheel to contain 12 teeth, of 3-inch arc pitch, and to gear with a wheel having 24 teeth?

Here number of teeth in wheel to be marked = 12, divided by the number of teeth (24) with which it gears; 12 ÷ 24 = .5. Now in column of ratios may be found ¹⁄₂ = .500 (which is the same thing as .5), and along the same horizontal line in the table, and in the column headed 12 (the number of teeth in the wheel) is found .34. This is the tabular value, which, multiplied by 3 (the arc pitch of the teeth), gives 1.02, which is the setting number on the graduated edge. It will be noted, however, that the graduated edge is marked 1, 2, 3, &c., and that between each consecutive division are ten subdivisions; hence, for the decimal .02 an allowance may be made by setting the line 1 a proportionate amount below the tangent line marked on the wheel to set the instrument by.

Required now the setting number for the wheel to have the 24 teeth.